Scanning tunneling microscopy and spectroscopy of finite-size twisted bilayer graphene

Finite-size twisted bilayer graphene (TBG, where here the TBG is of nanoscale size) is quite unstable and will change its structure to a Bernal (or $AB$-stacking) bilayer with a much lower energy. Therefore, the lack of finite-size TBG makes its electronic properties difficult to access in experiments. In this paper, a special confined TBG is obtained in the overlaid area of two continuous misoriented graphene sheets. The width of the confined region of the TBG changes gradually from about 22 to 0 nm. By using scanning tunneling microscopy, we study carefully the structure and the electronic properties of finite-size TBG. Our results indicate that the low-energy electronic properties, including twist-induced Van Hove singularities (VHSs) and spatial modulation of the local density of states, are strongly affected by the translational symmetry breaking of the finite-size TBG. However, the electronic properties above the energy of the VHSs are almost not influenced by quantum confinement even when the width of the TBG is reduced to only a single moiré spot.

Figure 1

(a) A typical STM topography of graphene bilayer with twisted angle $\theta \sim 2.9^{\circ }$ ($V_{\mathrm{sample}}=223\mathrm{mV}$ and $I=180\mathrm{pA}$). The period of the moiré pattern is about 4.9 nm. (b) Tunneling spectra recorded along the arrow of (a). (c) Theoretical calculated band structure (left panel) of twisted bilayer graphene with twisted angle $\theta \sim 2.9^{\circ }$ and the corresponding LDOS (right panel) with two VHSs (pointed out by the arrows).

Figure 2

(a)–(d) Conductance maps of twisted bilayer graphene with twisted angle $\theta \sim 2.9^{\circ }$ at VHS ($V=228\mathrm{mV}$), 393 mV, $-\mathrm{VHS}(V=-210\mathrm{mV})$, and $-309\mathrm{mV}$, respectively. (e)–(h) Theoretical calculated LDOS distribution at $\pm \mathrm{VHS}$ and away from them, respectively. (i) The profile lines along the dashed lines in (b) and (c). The positions of the strongest STS signal shift $D/2$. (j) The profile lines along the dashed lines in (f) and (g). The positions of the strongest STS signal shift $D/2$.

Figure 3

(a) STM image of a finite-size TBG with width decreasing from 22 to 0 nm ($V_{\mathrm{sample}}=-700\mathrm{mV}$ and $I=200\mathrm{pA}$). The twist angle of the TBG is about $2.1^{\circ }$ and the period of the moiré pattern is about 6.3 nm. (b) The schematic diagram to illustrate the structure of the confined TBG. (c) The side view of finite-size TBG on a SiC substrate. (d) The STS spectra measured along the arrow in (a). Right panel shows profile lines taken from the left panel. The intensities of the VHSs decrease gradually with decreasing the width of the TBG.

Figure 4

(a) STM image of finite-size TBG with $\theta \sim 2.1^{\circ }$ ($V_{\mathrm{sample}}=450\mathrm{mV}$ and $I=120\mathrm{pA}$). (b) Conductance maps of finite-size TBG at energies $-45$ and 245 meV. (c) The profile lines (blue and orange) taken from (b), explicitly showing the quantum confinement on the spatial distributions of the LDOS.